Efficient modeling of low- to mid-frequency vibration and power flow in complex structures.

Abstract

The investigation of low- to mid-frequency vibration transmission in complex structures requires the development of new methods for dynamic substructuring and power flow analysis, as well as the derivation of approximations for statistical analysis. In this work, the finite element model (FEM) of the full structure is divided into separate component FEMs, and component mode synthesis (CMS) is used to generate a reduced order model of the global structure. It is found that the Craig-Bampton method of CMS provides an excellent framework for predicting power flow. However, the cost of this CMS method is still prohibitive for a sufficiently fine mesh. Consequently, a secondary modal analysis reduction technique (SMART) is developed to further reduce the size of the CMS model. In particular, an eigenanalysis is performed on the constraint-mode partitions of the CMS mass and stiffness matrices. The resultant eigenvectors, which describe the characteristic motion of the interface, are called characteristic constraint (CC) modes. It is shown that the power flow is accurately calculated by a reduced order model with relatively few CC modes. Furthermore, a multi-level substructuring technique is presented for handling large FEMs. This involves a two-part partitioning scheme: first, the FEM is divided into component structures; second, each component structure is partitioned into subcomponents. After this partitioning, a CMS model of each component is built. Then the reduced order CMS model for the global structure is constructed by applying SMART and CMS to these component CMS models. In this manner, the flow of vibration energy can be tracked through the regions of interest in a complex structure using a highly reduced order model. After generating the reduced order model of a complex structure, the power flow statistics are calculated over an ensemble of systems due to the variation of system parameters. Each modal response is expanded in a series of globally orthogonal polynomials or locally linear interpolation functions in these parameters. Then the system equations are derived using Galerkin's method. This statistical treatment provides efficient and accurate modeling of parameter uncertainties, which is critical for mid-frequency vibration analysis.